Unlike the standard Leray spectral sequence, the perverse Leray spectral sequence has the wonderful property that it degenerates at the \(E_2\) -term for any projective morphism [1]} (see also [2]} for the same statement under much weaker assumptions). This gives a decomposition
\(H^k(Y,\mathbb {Q}) = \bigoplus _{p+q=k} E_2^{p,q}.\) 
